1. Field of the Invention
The present invention relates generally to magnetic sensors, more particularly, to extraordinary magnetoresistance (EMR) effect and Hall effect sensors and methods for making and using the same.
2. Description of the Related Art
Generally, there are at least two types of magnetic sensors that can be used to measure a magnetic field, including an EMR sensor and a Hall sensor. An EMR sensor operates based on an EMR effect. Broadly speaking, the EMR effect quantifies scattering of electrons at a material interface when an electric current is applied to the material. The scattering occurs due to an interaction between the magnetic field and electrons in at least one of the materials comprising the sensor. Generally, a the Hall effect quantifies a shearing force caused by interaction between the magnetic field and electrons in the current applied to the material. Each of these effects are described in greater detail in the sections below.
EMR Effect Sensors
EMR is a large magnetoresistance effect that may arise in a nonmagnetic semiconductor metal hybrid structure. In an EMR effect sensor, the Lorentz force induced by a magnetic field may cause a redistribution of the electric current density between adjacent semiconductor and metal layers resulting in resistance changes. The EMR effect may be described by equation (1):
                                              ⁢                              EMR            ⁡                          (                              H                e                            )                                =                                                    R                ⁡                                  (                  H                  )                                            -                              R                ⁡                                  (                  0                  )                                                                    R              ⁡                              (                0                )                                                                        (        1        )            where He is the external magnetic field (e.g., external to the sensor), R(H) is the measured resistance of the sensor in the presence of a magnetic field H, and R(0) is the measured resistance of the sensor at zero magnetic field.
The dimensions of an EMR sensor, the thickness of its layers, and the placement of the voltage and current leads may significantly effect magnitude of the measured EMR. FIG. 1A and FIG. 1B depict prior art EMR effect sensors 100A and 100B. As depicted in both figures, EMR effect sensors 100A and 100B each have a metal layer 102 and a semiconductor layer 104. In both pictures, the voltage and current leads are arranged symmetrically around center 110 of the EMR effect sensor.
Voltage leads 106 and current leads 108 are located on one side of the device—coupled to semiconductor layer 104. FIG. 1A depicts voltage leads 106 and current leads 108 in an V-I-I-V formation, and FIG. 2A depicts the voltage and current in a I-V-V-I formation. The voltage (V) between voltage leads 106 and the current (I) through current leads 108 allow for the calculation of the resistance R(H) in equation (1) by using equation (2):
                              R          ⁡                      (            H            )                          =                              V            ⁡                          (              H              )                                            I            ⁡                          (              H              )                                                          (        2        )            
EMR effect sensors 100A and 100B can further be described by width 112 of the metal layer 102, width 114 of the semiconductor layer 104, and length 116 of the EMR effect sensor. FIG. 2 illustrates the simulated EMR effect for EMR effect sensor 102B (e.g., having an I-V-V-I lead formation) for four different magnetic fields as a function of the length (L) 116 of the EMR sensor divided by the width (Ws) 114 of the semiconductor layer 104. In this example, metal layer 102 is gold, and semiconductor layer 104 is indium antimonide. As shown, the EMR effect is dependent on the dimensions of the sensor. In FIG. 2, the EMR effect reaches a maximum of approximately 1.1×105% with a 1 T magnetic field and an L/Ws ratio of 25.
FIG. 3A and FIG. 3B illustrate the change in current density in semiconductor layer 104 of EMR effect sensor 100B. At a zero magnetic field, the current density in semiconductor layer 4 is low, as depicted by minimal current density flux lines in semiconductor layer 104 in FIG. 3A. The presence of an external magnetic field causes a redistribution of the current density due to the Lorentz force yielding an increased current density in the semiconductor, as depicted by more current density flux lines in semiconductor layer 104 in FIG. 3B. In this example, a 0.3 T external magnetic field creates an increased current density within the semiconductor layer, and as a result, creates a higher electrical resistivity.
Hall Effect Sensors
The Hall effect is the production of a voltage difference (the Hall voltage) across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current. For an n-type semiconductor where there is a dominate type of charge carrier-electron, the Hall voltage VH is given by equation (3):
                              V          H                =                  -                      IB            ned                                              (        3        )            where I is the current input, B is the magnetic flux density, d is the thickness of the plate, e is the electron charge, and n is the carrier density of electrons.
The most frequently used Hall effect sensor consists of a high mobility semiconductor conductive bar with four or six contacts. Two of the contacts are current leads, which are used to induce a current flow through the Hall bar, and the other contacts are voltage probes which are used to measure the Hall voltage. FIG. 9 depicts the typical four contacts Hall effect sensor 900. As depicted in the figure, Hall effect sensors 900 have a semiconductor bar 901 and voltage probes 902 and current leads 903 are located on the edges of the semiconductor bar 901. The voltage probes are arranged symmetrically along the centerline 904 of the Hall sensor.
The Hall sensitivity SH is a very useful parameter for judging the performance of the Hall sensor (equation (4)).
                              S          H                =                                            ∂                              V                H                                                    ∂              B                                =                      -                          I              ned                                                          (        4        )            
The Hall sensitivity is typically 1˜5 mV/mT for a 1 mA current with the commercial Hall sensors.
Another useful parameter is the thermal field noise (in T/√Hz, equation (5)):
                                          S            B                          =                                            4              ⁢                              K                B                            ⁢              TR                                            S            H                                              (        5        )            where R is the resistance of the Hall sensor, T is the temperature and KB is the Boltzmann constant. Two-dimensional quantum-well multilayer heterostructures based on GaAs are promising for low-noise Hall sensors with 100 nT/√Hz. In general, noise could be significantly reduced with devices of lower resistance.